APPL ICATION OF SOME ACTUAL EVAPOTRANSPIRATION MODELS IN SIMULATION OF SOIL MOISTURE

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1 RESOURCES SCIENCE Vol. 23 No. 6 Nov ( ; ) Penman Priestley2Taylor Penman2Menteith Shuttleworth2Wallace Penman Priestley2Taylor ; Shuttleworth2Wallace Penman2Menteith ; Penman2Menteith ; ; ; S B (2001) APPL ICATION OF SOME ACTUAL EVAPOTRANSPIRATION MODELS IN SIMULATION OF SOIL MOISTURE LU Hou2quan 1 YU Gui2rui 2 (1. Chinese Academy of Meteorological Sciences Beijing China ; 2. Institute of Geographical Sciences and Natural Resources Research CAS Beijing China) Abstract Based on experiments in the field a comparison of modified referenced evapotranspiration model such as Penman model and Priestley2Taylor model actual evapotranspiration model such as Penmen2Men2 teithin model for closed canopy and Shuttleworth2Wallace model for sparse canopy is made. Observed data of soil moisture in two years of different climatic patterns is used to simulate the variation of soil moisture. The results show that in dry years the fitness of four models is better than that in rainy years especially for dy2 namical models. In rainy years when maize plants fully grow the fitness of Shuttleworth2Wallace model is better than that of Penman2Menteith model but in dry years when leaf area is bigger the fitness of Penman2 model is better. Comparatively fitness of modified referenced evapotranspiration models is stable owing to those models including parameters of soil moisture. There are many parameters in dynamical models among which some parameters are not observed. Therefore when maize plant is small and the moisture content in surfaces of both leaves and soil varied frequently the fitness of dynamical models is unstable. The results al2 so show that the fitness of variation of soil moisture content simulated by using environmental factors is reason2 able in a certain time scale and a big accumulated error will appear on a long time scale over one month. Key words Actual evapotranspiration ; Soil moisture content ; Evapotranspiration model ; Climatic pattern of year ; (1957 )

2 ( EKO MR221) ( EKO CN211) 2 m 5cm 0. 5m 2m 0. 5m 2m 2m ; (3 ) cm Penman Priestley2Taylor ; 100cm 10cm Penman2Menteith Shuttleworth2Wallace Stannard [1 ] Penman2Menteith Shuttleworth2Wal2 lace Priestley2Taylor (LI Priestley2Taylor Shuttle2 worth2wallace Penman2Menteith ; Kustas [2 ] Penman2Menteith 311 Penman [3 Priestley2Taylor Penman ] Priestley2Taylor E t = R n + E 0 (1) + E t (mm) ; R n (mm d - 1 ) ; Penman Priestley2 (hpaπ ) ; - Taylor Penman2Menteith (hpa K - 1 ) ; E 0 (mm) Shuttleworth2Wallace E 0 = ( u 2 ) ( e s - e a ) (2) u 2 2m (m s - 1 ) e s e a 2m 2 (35 47 N E) 600m 2 (20m 30m) E a = ( W k - W p ) 1 - exp ( Zea mays L. ) hm - 2 ( 70 cm 40 cm) cm % ; cm % ; ) (hpa) [4 ] E t j W k W j E t j W j - W p Wk < W j E a (mm) E t j ; W k W j ; W p 312 Priestley2Taylor Priestley2Taylor [5 ] (3)

3 ( ) r s E = + ( R n - G) (4) E (MJ m - 2 d - 1 ) ; G [9 ] (MJ m - 2 d - 1 ) ; ( = 1. 26) E a = E t 1 - exp W W k (5) Q E t Priestley2Taylor (mm) W 5cm p (mol m - 2 s - 1 ) Q p = 747 S (14) W k 5cm S (kw m - 2 ) [7 314 Shuttleworth2Wallace ] Davies Shuttleworth Wallace [10 ] (5) E a = E exp W W k x (6) W W k 30cm E = C c PM c + C s PM s (15) x PM c = A + ( C pd - r c aa s )Π( r a a + r c a) (16) + [1 + rsπ( c r a Lu [8 ] a + r c a) ] ( x) PM s = A + [ C pd - r s a ( A - A s ) ]Π( r a a + r s a) (17) + [1 + r s sπ( r a a + r s a) ] C c = [1 + R c R a ΠR s ( R c + R a ) ] - 1 (18) 313 Penman2Menteith Menteith Penman R s = ( + ) r s a + r s s (21) E = ( R R n - G) + C p ( c = ( + ) r c a + r c s (22) e s - e a )Πr a (7) + (1 + r s )Πr a E (MJ m - 2 d - 1 ) ; R n (MJ m - 2 ) ; ; D (hb) ; r a a m - 2 d - 1 ) ; G (MJ m - 2 d - 1 ) ; r s (s m - 1 ) ; r s a (s m - 1 ) ; r a ( s m - 1 ) ; ; r s s ; r c a (kg m - 3 ) ; C p (MJ kg - 1 K - 1 ) ; e s ; r c s (7) r s (hpa) ; e a s m - 1 (hpa) A = R n - G (23) r a = [ln{ ( Z - d)πz 0} ] 2 k 2 1 A s = R s n - G (24) (8) u R n R s n (W m - 2 ) G Z ( = 2 m) ; d (m) ; Z 0 (W m - 2 ) (m) ; k Karman ( = 0. 41) ; u 2m (m s - 1 ) d Z 0 h (m) d = h (9) Z 0 = h (10) r s = G - 1 ΠL (11) G (s m - 1 ) L Davies(1973) [6 ] Priestley2 Taylor G = ( Q p )Π( Q p ) (12) G = Q p (13) C s = [1 + R s R a ΠR s ( R s + R a ) ] - 1 (19) R a = ( + ) r a a (20) A A s (W R s n = R n exp ( - CL) (26) C ( = 0. 7 [11 ] ) L = { e w ( T x ) - e w ( T 0 ) }Π( T x - T 0 ) (27) e w ( T x ) e w ( T 0 ) T x T 0 (hpa K - 1 ) T x T 0

4 ( K) r c a = r b Π2L (28) r b = (100Πn) ( wπuh) 1Π2 [1 - exp ( nπ2) ] - 1 (29) r b ; w (m) n ( = 2. 5 ) u h (m s - 1 ) 0 L 4 r a a = 1 4 Lra a ( ) (4 - L) ra a (0) (30) r s a = 1 4 Lrs a ( ) (4 - L) rs a (0) (31) r a a ( ) r a a (0) (L = 4) Penman Priestley2Taylor r s a ( ) 1 E t P2T Priest2 r s a (0) ( L = 4) ley2taylor P Penman Priest2 (s m - 1 ) ley2taylor Pen2 man 1994 Penman 10 % r a a ( ) = [exp ( - z 0 Πh) - exp{ - n ( Z 0 + d)πh} ] hexp ( n) nk h r s a ( ) = 1 ln z r - d p ku 3 h - d p (32) + h nk h [exp{ n[1 - ( Z 0 + d)πh ]} - 1 ] (33) r s a (0) = ln( z r Πz 0 ) ln{ ( d p + z 0 )Πz 0 }Πk 2 u (34) r a a (0) = ln 2 ( z r Πz 0 )Πk 2 ur s a (0) (35) d p (m) h (m) z 0 ( = 0. 01m) c d [10 ] n ( = 2. 5 ) ( Z 0 + d) (m) z r ( = 2m) Z 0 d Penman2Menteith 3 Shut2 tleworth Gurney [10 ] z 0 d p = 1. 1 hln(1 + X 1Π4 ) (36) = z h X 1Π2 0 < X < 0. 2 (37) X = c d L (38) K h = ku 3 ( h - d) (39) u 3 = kuπln{ ( z r - d)πz 0 } (40) K h (m 2 s - 1 ) u 3 (m s - 1 ) u 10 cm ( pf = 1. 8) r s s = 0. 02m s - 1 ; r s s = 0 ; ( pf = 318) r s s = 2000m s - 1 2m (m s - 1 ) Camillo [11 ] Fig. 1 Comparison of potential evapotranspiration calculated by Penman model and Priestley2Taylor model in different years 10 cm r s s = 0 > p = p (41) < p r s s (cm s - 1 ) 10cm (mm) % Penman 1 Penman Priestley2Taylor

5 Shuttleworth2Wallace Priestley2Taylor (1994 ) 1 ; Priestley2Taylor (1995 ) (1994) (1995) ; Penman 1994 ; M n + P n > M c 2 M n + 1 = M c Fig. 2 Comparison of actual evapotranspiration calculated ( F 1 n ) by different models 4. 2 F 1 n = K( ) ( d Πdz) (43) 2 K( ) d Πdz E a P2M Penman2 Monteith S2W Shuttleworth2Wallace pf 3. 0 Priestley2Taylor ( 6) x K( ) = 0 ; pf 1. 8 K 5 ;Penman ( 3) j 0. 6 ( ) = 1. 2 mm d - 1 ; (100 cm ) = a - b (44) (mm) ; a b ; 2a Penman2Monteith 1995 (42) ; 1994 Shuttleworth Wallace ; 1 Shuttleworth2Wallace ; Penman Priestley2Taylor ; 2 (1994) Shuttleworth2Wallace 4. 3 M n+1 = M n + P n - [ E tn + ( D 2 n - D 1 n ) + ( F 2 n - F 1 n ) ] Penman2Monteith (1995) Penman2Monteith Penman2Monteith (42) M n M n + 1 n n + 1 (mm) ; P n n (mm) ; E tn (mm) ; D 2 n D 1 n (mm) ; F 1 n F 2 n (mm) 30cm ( M c )

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